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*To*: tesla@xxxxxxxxxx*Subject*: RE: The "second pig" ballast: Questions.*From*: "Tesla list" <tesla@xxxxxxxxxx>*Date*: Wed, 09 Feb 2005 06:48:13 -0700*Delivered-to*: testla@pupman.com*Delivered-to*: tesla@pupman.com*Old-return-path*: <teslalist@twfpowerelectronics.com>*Resent-date*: Wed, 9 Feb 2005 06:49:09 -0700 (MST)*Resent-from*: tesla@xxxxxxxxxx*Resent-message-id*: <TS0QnD.A.crE.SThCCB@poodle>*Resent-sender*: tesla-request@xxxxxxxxxx

Original poster: "Steve Conner" <steve.conner@xxxxxxxxxxx>

>This is the very subject Ive been trying to learn about recently and I'm a >little confused as to what you mean by "it impossible to make an efficient >ballast no matter what number of turns you use".

Hi Gerry,

I found it very difficult back when I was learning too. I had to experiment with using old transformers as ballasts to convince myself. I seem to remember I was trying to use them as ballasts for fluorescent tubes. What I found was that as the number of turns was decreased, they went straight from drawing a tiny current that hardly lit the tube at all, to saturating and destroying the tube.

>Seems >like the flux density in the core is a function of the cross sectional >area. the volts per turn and frequency, and not dependent on the presence >of an airgap. Would this be correct??

I think this is true, but only if the coil were driven from a constant voltage source, like a transformer primary connected to the mains. The reason is that the Faraday's law induced EMF must always be equal to the drive voltage (if the coil is an ideal one with zero resistance) and hence the constant voltage forces constant flux density.

In this case, as the airgap was widened, the flux density would stay constant but the magnetizing current would go up. As the reluctance of the magnetic path is increased, it takes more magnetomotive force to produce a given flux density.

If you think about it, this line of thought proves the efficiency of the airgap. Widening the airgap will not cause saturation since the flux density stays constant. But it will decrease L, and I will increase in proportion (since with the constant voltage drive, I=V/X_L)

But the energy storage in the core is proportional to L*I^2. If we assume that L goes down as I goes up (so L=some constant/I) then the equation turns out as energy storage=some constant*I.

This proves that as the airgap is widened the energy storage capability of the core increases even though the maximum flux density stays constant.

Now taking this to its logical conclusion, you might think that the best inductor is a completely air cored one because it would be able to store infinite energy. But the resistance of the coil (which we ignored in this analysis) messes things up. So it turns out that adding some iron usually makes a more efficient coil, as it gives more inductance for a given length of wire (and hence resistance)

As an interesting aside- Superconducting air cored coils can in fact store colossal amounts of energy. The amounts would be infinite except there is a critical flux density beyond which the superconductor loses its magic properties.

Steve C.

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